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Bakushinskii Anatolii Borisovich

Publications in Math-Net.Ru

  1. On the achievable level of accuracy in solving abstract ill-posed problems and nonlinear operator equations in Banach space

    Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 3,  21–27
  2. Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing

    Matem. Mod., 34:5 (2022),  3–26
  3. Fast solution algorithm for a three-dimensional inverse multifrequency problem of scalar acoustics with data in a cylindrical domain

    Zh. Vychisl. Mat. Mat. Fiz., 62:2 (2022),  289–304
  4. Numerical solution of an inverse multifrequency problem in scalar acoustics

    Zh. Vychisl. Mat. Mat. Fiz., 60:6 (2020),  1013–1026
  5. Direct and converse theorems for iterative methods of solving irregular operator equations and finite difference methods for solving ill-posed Cauchy problems

    Zh. Vychisl. Mat. Mat. Fiz., 60:6 (2020),  939–962
  6. Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain

    Sib. Zh. Vychisl. Mat., 22:4 (2019),  381–397
  7. Low-cost numerical method for solving a coefficient inverse problem for the wave equation in three-dimensional space

    Zh. Vychisl. Mat. Mat. Fiz., 58:4 (2018),  561–574
  8. Iteratively regularized Gauss–Newton method for operator equations with normally solvable derivative at the solution

    Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 8,  3–11
  9. Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015),  1637–1645
  10. New a posteriori error estimates for approximate solutions to iregular operator equations

    Num. Meth. Prog., 15:2 (2014),  359–369
  11. On a complete discretization scheme for an ill-posed Cauchy problem in a Banach space

    Trudy Inst. Mat. i Mekh. UrO RAN, 18:1 (2012),  96–108
  12. On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces

    Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012),  483–498
  13. Convergence rate estimation for finite-difference methods of solving the ill-posed Cauchy problem for second-order linear differential equations in a Banach space

    Num. Meth. Prog., 11:1 (2010),  25–31
  14. A rate of convergence and error estimates for difference methods used to approximate solutions to ill-posed Cauchy problems in a Banach space

    Num. Meth. Prog., 7:2 (2006),  163–171
  15. Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton–Kantarovich scheme

    Sib. Zh. Vychisl. Mat., 7:1 (2004),  1–12
  16. An iteratively regularized gradient method for solving nonlinear irregular equations

    Zh. Vychisl. Mat. Mat. Fiz., 44:5 (2004),  805–811
  17. Stable gradient design method for inverse problem of gravimetry

    Matem. Mod., 15:7 (2003),  37–45
  18. On some inverse problem for a three-dimensional wave equation

    Zh. Vychisl. Mat. Mat. Fiz., 43:8 (2003),  1201–1209
  19. Iterative Newton-type methods with projecting for solution of nonlinear ill-posed operator equations

    Sib. Zh. Vychisl. Mat., 5:2 (2002),  101–111
  20. Convergence rate of iterative regularization algorithms for linear problems with convex constraints

    Zh. Vychisl. Mat. Mat. Fiz., 42:7 (2002),  933–936
  21. On iterative methods of gradient type for solving nonlinear ill-posed equations

    Sib. Zh. Vychisl. Mat., 4:4 (2001),  317–329
  22. Conditions of sourcewise representation and rates of convergence of methods for solving ill-posed operator equations. Part II

    Num. Meth. Prog., 2:1 (2001),  65–91
  23. Conditions of sourcewise representation and rates of convergence of methods for solving ill-posed operator equations. Part I

    Num. Meth. Prog., 1:1 (2000),  62–82
  24. Gradient-type iterative methods with projection onto a fixed subspace for solving irregular operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 40:10 (2000),  1447–1450
  25. Necessary conditions for the convergence of iterative methods for solving irregular nonlinear operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 40:7 (2000),  986–996
  26. Iterative regularization algorithms for monotone variational inequalities

    Zh. Vychisl. Mat. Mat. Fiz., 39:4 (1999),  553–560
  27. Iterative methods of gradient type of irregular operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 38:12 (1998),  1962–1966
  28. On the rate of convergence of iterative processes for nonlinear operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 38:4 (1998),  559–563
  29. Iterative methods for the solution of nonlinear operator equations without the property of the regularity

    Fundam. Prikl. Mat., 3:3 (1997),  685–692
  30. Linear approximation of the solutions of nonlinear operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 36:9 (1996),  6–12
  31. Iterative methods without saturation for solving degenerate nonlinear operator equations

    Dokl. Akad. Nauk, 344:1 (1995),  7–8
  32. Note on the regularizing properties of methods of conjugate directions

    Zh. Vychisl. Mat. Mat. Fiz., 34:3 (1994),  481–483
  33. Iterative methods for solving nonlinear operator equations without regularity. A new approach

    Dokl. Akad. Nauk, 330:3 (1993),  282–284
  34. The problem of the convergence of the iteratively regularized Gauss–Newton method

    Zh. Vychisl. Mat. Mat. Fiz., 32:9 (1992),  1503–1509
  35. On the theory of approximate methods for solving an ill-posed abstract Cauchy problem

    Dokl. Akad. Nauk SSSR, 312:4 (1990),  777–782
  36. Fast linear iterative algorithms of image restoration

    Zh. Vychisl. Mat. Mat. Fiz., 28:6 (1988),  933–937
  37. Rough conjugate directions methods

    Zh. Vychisl. Mat. Mat. Fiz., 27:12 (1987),  1763–1770
  38. Iterative regularizing algorithms for nonlinear problems

    Zh. Vychisl. Mat. Mat. Fiz., 27:4 (1987),  617–621
  39. Remarks on the choice of regularization parameter from quasioptimality and relation tests

    Zh. Vychisl. Mat. Mat. Fiz., 24:8 (1984),  1258–1259
  40. An asymptotic relation for the iteratively regularized Newton–Kantorovich method

    Zh. Vychisl. Mat. Mat. Fiz., 23:1 (1983),  216–218
  41. Principle of the residual in the case of a perturbed operator for general regularizing algorithms

    Zh. Vychisl. Mat. Mat. Fiz., 22:4 (1982),  989–993
  42. Some nonstandard regularizing algorithms and their numerical realization

    Zh. Vychisl. Mat. Mat. Fiz., 22:3 (1982),  532–539
  43. Equivalent transformations of variational inequalities and their use

    Dokl. Akad. Nauk SSSR, 247:6 (1979),  1297–1300
  44. On the principle of iterative regularization

    Zh. Vychisl. Mat. Mat. Fiz., 19:4 (1979),  1040–1043
  45. Optimal and quasi-optimal methods for the solution of linear problems that are generated by regularizing algorithms

    Izv. Vyssh. Uchebn. Zaved. Mat., 1978, no. 11,  6–10
  46. Methods for the solution of monotone variational inequalities that are based on the principle of iterative regularization

    Zh. Vychisl. Mat. Mat. Fiz., 17:6 (1977),  1350–1362
  47. A regularizing algorithm on the basis of the Newton–Kantorovič method for the solution of variational inequalities

    Zh. Vychisl. Mat. Mat. Fiz., 16:6 (1976),  1397–1404
  48. The stability and domain of convergence of certain regularizing algorithms

    Zh. Vychisl. Mat. Mat. Fiz., 16:1 (1976),  228–232
  49. Methods of stochastic approximation type for the solution of linear ill-posed problems

    Sibirsk. Mat. Zh., 16:1 (1975),  12–18
  50. On the solution of variational inequalities

    Dokl. Akad. Nauk SSSR, 219:5 (1974),  1038–1041
  51. A remark on a class of regularizing algorithms

    Zh. Vychisl. Mat. Mat. Fiz., 13:6 (1973),  1596–1598
  52. The problem of constructing linear regularizing algorithms in Banach spaces

    Zh. Vychisl. Mat. Mat. Fiz., 13:1 (1973),  204–210
  53. Difference methods of solving ill-posed Cauchy problems for evolution equations in a complex $B$-space

    Differ. Uravn., 8:9 (1972),  1661–1668
  54. The solution by difference methods of an ill-posed Cauchy problem for a second order abstract differential equation

    Differ. Uravn., 8:5 (1972),  881–890
  55. Difference schemes for the solution of ill-posed abstract Cauchy problems

    Differ. Uravn., 7:10 (1971),  1876–1885
  56. Stabilization of solutions of linear differential equations in Hilbert space

    Mat. Zametki, 9:4 (1971),  415–420
  57. Remarks on the Kupradze–Aleksidze method

    Differ. Uravn., 6:7 (1970),  1298–1301
  58. On extending the principle of the residual

    Zh. Vychisl. Mat. Mat. Fiz., 10:1 (1970),  210–213
  59. The construction of regularizing algorithms in the case of random noise

    Dokl. Akad. Nauk SSSR, 189:2 (1969),  231–233
  60. Regularization algorithms for linear equations with unbounded operators

    Dokl. Akad. Nauk SSSR, 183:1 (1968),  12–14
  61. Some properties of regularizing algorithms

    Zh. Vychisl. Mat. Mat. Fiz., 8:2 (1968),  426–429
  62. The solution of some integral equations of the first kind by the method of successive approximation

    Zh. Vychisl. Mat. Mat. Fiz., 8:1 (1968),  181–185
  63. A general method of constructing regularizing algorithms for a linear incorrect equation in Hilbert space

    Zh. Vychisl. Mat. Mat. Fiz., 7:3 (1967),  672–677
  64. A numerical method for solving Fredholm integral equations of the 1st kind

    Zh. Vychisl. Mat. Mat. Fiz., 5:4 (1965),  744–749
  65. A method of solving “degenerate” and “almost degenerate” linear algebraic equations

    Zh. Vychisl. Mat. Mat. Fiz., 3:6 (1963),  1113–1114
  66. The method of potentials and the numerical solution of Dirichlet' s problem for the Laplace equation

    Zh. Vychisl. Mat. Mat. Fiz., 3:3 (1963),  574–580

  67. Correction to: “On the problem of linear approximation of solutions of nonlinear operator equations”

    Zh. Vychisl. Mat. Mat. Fiz., 39:4 (1999),  704
  68. Numerical solution of ordinary and partial differential equation. Ed. L. Fox . Book Review

    Zh. Vychisl. Mat. Mat. Fiz., 4:3 (1964),  615–617

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